Oh Kate, that's a shame (adjoining wall). How on earth did it get in?
I'd go next door and tell them to take a brick or 2 out of the wall, their side (you don't want the hassle). Explain to them that the prevailing winds will precipitate an updraught in a Northerly direction (or Southerly, or whichever direction they are from you) and if the bird dies
they will have the resulting smell. Do this in your best scientist voice, as though you really know what you're talking about, and it
might work.
